Making and Sharing K-Dual Frame Pairs. (4th December 2021) - Li, Ya-Nan; Li, Yun-Zhang
Abstract: The atomic decomposition of signals is one of the most important problems in the frame theory. K -dual frame pairs may be used to stably reconstruct elements from the range of bounded linear operators on Hilbert spaces. The purpose of this paper is making K -dual frame pairs and finding common K -dual Bessel sequence. We present a sufficient condition on operators on H which takes a K -dual frame pairs to other ones; characterize bounded linear operators on l 2 ( J ) that transform K -dual frame pairs to other ones; prove that two Bessel sequences can always be extended to a K -dual frame pair, and that two orthogonal K -frames have a common K -dual Bessel sequence under certain conditions; and obtain a sufficient condition which the K -duals of one K -frame is contained in the ones of another K -frames. Abundant examples are also provided to illustrate the generality of the theory.